Coupling and Convergence for Hamiltonian Monte Carlo

Autor:	Bou-Rabee, Nawaf, Eberle, Andreas, Zimmer, Raphael
Rok vydání:	2018
Předmět:	Mathematics - Probability Statistics - Computation Statistics - Machine Learning 60J05 65P10 65C05
Zdroj:	Ann. Appl. Probab., Volume 30, Number 3 (2020), 1209-1250
Druh dokumentu:	Working Paper
DOI:	10.1214/19-AAP1528
Popis:	Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal target distributions are included. Explicit quantitative bounds for the number of steps required to approximate the stationary distribution up to a given error are a direct consequence of contractivity. These bounds show that HMC can overcome diffusive behaviour if the duration of the Hamiltonian dynamics is adjusted appropriately. Comment: 50 pages, 8 figures, extended the coupling approach to include corresponding results under a Foster-Lyapunov condition
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1805.00452 Zobrazit plný text záznamu View this record from Arxiv